I started by thinking about daily flights and tried to work backward from there.
Start by clarifying the scope (e.g., commercial flights, all aircraft) and then use a top-down estimation approach. Break the problem into manageable components: total daily flights, average flight duration, and the distribution of flights over time. Calculate the average number of planes in the air at any moment by multiplying the rate of takeoffs by the average duration, or by using Little's Law.
Pro tip: State your assumptions explicitly and round numbers to make calculations easier. Emphasize that the goal is to demonstrate structured thinking, not to get the exact number. If time permits, mention that you could validate with data sources like FAA or FlightAware.
Ask clarifying questions to define the scope: Are we counting only commercial passenger planes, or all aircraft including private, cargo, and military? Are we considering the entire US airspace or just the continental US? This shows you think critically about the problem.
Estimate the number of flights departing from US airports per day. You can start with the number of major airports, average flights per airport per day, and adjust for smaller airports. Alternatively, use known statistics: approximately 45,000 flights per day in the US (pre-COVID).
Estimate the average duration of a flight. Domestic flights might average 2-3 hours, but include international flights departing from the US which can be longer. A reasonable average might be 3 hours.
Use Little's Law: Average number in system = arrival rate × average time in system. Convert daily flights to hourly: 45,000 / 24 ≈ 1,875 flights per hour. Multiply by average duration (3 hours) to get approximately 5,625 planes in the air at any moment. Adjust for peak vs. off-peak if needed.
Check if the number seems reasonable. Consider that not all planes are in the air simultaneously due to scheduling; there are peak hours. You might adjust by noting that flights are not uniformly distributed, so the average might be slightly lower or higher. Also, consider if you're including all aircraft types.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.